Subgroups — #27165834

Order 12832.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20264378	C₂	1	2	yes	maximal, complemented
2	#20264374	C₂	1	1	yes	maximal, characteristic
3	#15692006	C₄	1	1	yes	characteristic
4	#15692006	C₂²	1	1	yes	characteristic
5	C₄×D₄₀₁	C₄	1	1	yes	characteristic
6	C₂×D₄₀₁	C₈	1	1	yes	characteristic
7	C₄×C₄₀₁	C₈	1	1	yes	characteristic
8	Dic₄₀₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄₀₁	C₂×C₈	1	1	yes	characteristic
10	D₄₀₁	—	2	1	no	—
11	C₄₀₁	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	401	1	no	maximal, Sylow
13	C₂×C₈	—	401	1	no	—
14	C₁₆	—	401	2	no	—
15	C₂×C₄	—	401	1	no	—
16	C₈	—	401	1	no	—
17	C₈	—	401	1	no	—
18	C₂²	—	401	1	no	—
19	C₄	—	401	1	no	—
20	C₄	#15692008	1	1	yes	characteristic
21	C₂	—	802	1	no	—
22	C₂	C₂×#15692008	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20264378	C₂	semidirect
11. C₄₀₁	M₃₂	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.